Correlating Structural Properties with Electrochemical Behavior of Non-graphitizable Carbons in Na-Ion Batteries

We report on a detailed structural versus electrochemical property investigation of the corncob-derived non-graphitizable carbons prepared at different carbonization temperatures using a combination of structural characterization methodology unique to this field. Non-graphitizable carbons are currently the most viable option for the negative electrode in sodium-ion batteries. However, many challenges arise from the strong dependence of the precursor’s choice and carbonization parameters on the evolution of the carbon matrix and its resulting electrochemistry. We followed structure development upon the increase in carbonization temperature with thorough structural characterization and electrochemical testing. With the increase of carbonization temperature from 900 to 1600 °C, our prepared materials exhibited a trend toward increasing structural order, an increase in the specific surface area of micropores, the development of ultramicroporosity, and an increase in conductivity. This was clearly demonstrated by a synergy of small- and wide-angle X-ray scattering, scanning transmission electron microscopy, and electron-energy loss spectroscopy techniques. Three-electrode full cell measurements confirmed incomplete desodiation of Na+ ions from the non-graphitizable carbons in the first cycle due to the formation of a solid–electrolyte interface and Na trapping in the pores, followed by a stable second cycle. The study of cycling stability over 100 cycles in a half-cell configuration confirmed the observed high irreversible capacity in the first cycle, which stabilized to a slow decrease afterward, with the Coulombic efficiency reaching 99% after 30 cycles and then stabilizing between 99.3 and 99.5%. Subsequently, a strong correlation between the determined structural properties and the electrochemical behavior was established.


X-ray powder diffraction measurements
Raw data from XRD measurements was fitted with Origin software and all of the calculated structural parameters were based on the results of the fitting. Raw data and its corresponding fits are shown in Figure S2.
The interlayer spacing was calculated from Bragg's law: 1 (eq. S1) = 2 The height of graphene layer stack, L C is calculated by: 2 (eq. S2) = 0.9 * (002) * cos (002) where is the wavelength and FWHM is the full width half maximum value corresponding to the (002) basal plane.
Average number of graphene layers is determined as the ratio of the height of the graphene layer stack and the interlayer spacing ( . / ) + 1

Raman spectroscopy -defined the concentration of defects
To quantify the structural order with Raman spectroscopy, we defined the concentration of defects (α) as: 3 (eq. S3) = where I G is the integrated area of the G-band (∼1580 cm −1 ) and I D is the area of the D band (∼1350 cm -1 ).

Small-Angle X-Ray Scattering Measurements
The SAXS measurements were performed by an in-lab-modified Kratky-type camera (Anton Paar KG, Graz, Austria), which was attached to the conventional generator (GE Inspection Technologies, SEIFERT ISO-DEBYEFLEX 3003) with a Cu-anode operating at 40 kV and 50 mA (Cu-line with = 1.54 Å). The camera was equipped with a Goebel mirror (Osmic MAX-FLUX# focusing multilayer optics), which served as a monocromator and focusing element for the primary X-ray beam, and a block-collimation unit, which provided a well-defined, line-collimated primary beam. Correspondingly, the obtained SAXS data were experimentally smeared. The samples were placed between the two sheets of Scotch ® tape in S3 a 0.5 mm thick sample holder and were positioned in the primary beam in an evacuated SAXS camera (pressure between 2 and 4 mbar). The measurements were performed at 25°C with the total sampling time of 3 minutes per sample utilizing the Mythen 1K microstrip solid-state diode-array detector (Dectris, Baden, Switzerland) in the small-angle regime of scattering vectors from 0.08 < < 7 nm -1 , where . The SAXS data were q subsequently corrected for the Scotch ® tape and background scattering and were desmeared utilizing the so-called primary beam width and length profiles and the well-known iterative desmearing procedure introduced by Lake. 4 The desmeared SAXS data was then put to the absolute scale using water as a secondary standard 5 and further extended by the XRD data to obtain the overall SWAXS curves in the regime of the scattering vectors from 0.08 < < 24 nm -1 . These SWAXS curves were on absolute scale and were in units of cm -1 . q

Small-and Wide-Angle X-Ray Scattering Data Fitting
The SWAXS data of the non-graphitizable carbon samples studied were fitted according to the approaches described by Saurel et al. in ref. 6 . For the convenience of the interested reader, we provide below only a brief explanation of the fitting procedure used and encourage the reader to search the original publication for the details. In the framework of this procedure, the total SWAXS scattering intensity can be described as the sum of three different scattering contributions covering the three different characteristic length scales that can be resolved from the hierarchical structure of the studied non-graphitizable carbon samples ( Figure 2 in main article). Region I of this hierarchical structure is micrometer-sized carbon particles with a more or less rough surface. Region II is the nanometer-sized pores inside these microparticles, and the most detailed region III is the lamellar or so-called crumpled lamellar structure of carbon on the atomic scale. The total SWAXS scattering intensity, , in units of cm 2 where is the structural density of the non-graphitizable carbon samples, pores is the struc   volume fraction of nanometer-sized micropores, is the scattering length density of SLD  carbon with respect to vacuum, which is related to the scattering contrast of the pores and is related to through the relation ; is the pore-to-pore distance, and is the characteristic correlation length of the spatial pore distribution. This model was  derived for the two-phase system with the characteristic mean distance between the domains of the two phases, , where the parameter represents the so-called amphiphilic factor, which d a f in this case can be interpreted as related to disorder in the system: 6 (eq. S7) Based on this scattering contribution one can also estimate the radius of the micropores, , and r the surface area of the pores, At this point we must stress that the average pore radius calculated in this way is accurate only for spheroid pores in the low pore concentration limit, when f a = 0.4 (i.e. when ).
More generally, on the basis of the Babinet principle 9 an expression for the average pore-width, , and an estimate of the average width of the carbon matrix, , can be obtained from the p w C w Teubner-Stray form factor according to the expressions: and are the pore and carbon matrix effective lengths, respectively, which p w C w can be considered as a good estimation of their respective average widths.
The third contribution in eq. S4 can be written as: 6 , (eq. S10) where is an intensity scaling factor, the Voigt peak profile function, the local fluctuation of the interlayer distance due to the local distortions of the 2 z  structure, 10 the length below which the layers can be considered as effectively flat, the R  fractal cut-off length -above the curvature becomes random; and the fractal dimension. The  (eq. S12) The values of these structural parameters are gathered in Table S2.
Our experimental SWAXS curves were given in units of cm -1 and would have to be normalized by the sample density to obtain the total SWAXS scattering intensity, , curves in units SWAXS I of cm 2 g -1 . The sample density of the non-graphitizable carbon sample is difficult to determine because it depends on the volume fraction of the pores, which is a fitting parameter. However, according to Eq. (S11), the determination of the structural density is quite straightforward.
Therefore, in our study we fitted the SWAXS curves in units of cm -1 and multiplied the righthand side of Eq. (S4) with the Eq. (S12) accordingly.  Figure S1: XRD patterns of corncob derived non-graphitizable carbons prepared at different temperatuers of carbonization. The (002) and (100)

Note 1. Raman spectroscopy
Raman spectroscopy is a powerful tool to investigate the concentration of defects of the carbon materials. Two peaks may be observed ( Figure S5a), namely the D band (1350 cm -1 ) and the G band (1600 cm -1 ). For Corn@1600°C there is also a 2D peak present at 2670 cm -1 , indicating the presence of few layer graphene-like structures. Concentration of defects was determined as the ratio of the integrated areas of the D and G band peaks. The values are presented in Table 1. The concentration of defects (I D /I G ratio) decreases with the increasing temperature of carbonization, indicating the graphitization of the material to some extent ( Figure S5b). These results are in a good agreement with the data obtained by XRD. However, the I D /I G ratio is used to determine the concentration of defects in graphitic materials and is less accurate for non-graphitizable carbons. 13 S14 Figure Figure 4b in the main article. Figure S10: Correlation between the a) galvanostatic curves and b) correlation length describing the long-range order () and locally flat sections of the layers (R) with the relative plateau capacity and c) average pore width (W p ) and pore volume fraction (Φ p ) with the relative plateau capacity of corncob derived non-graphitizable carbons at different temperatures of carbonization. The relative plateau capacities were calculated according to the second discharge as presented in Figure 4b in the main article.

S21
S22 Figure S11: a) Statistical analysis of a particle size distribution from SEM images containing 13713 particles on a 2900 m 2 surface area. SEM images of the same location with different detectors b) ETD detector and c) ICE detector at 2.00 kV. SEM images of two different location with d) ETD detector at 5.00 kV and e) ICE detector at 5.00 kV. f) Magnification of the statistical analysis of a particle size distribution from 0 to 1000 nm and g) Magnification of the statistical analysis of a particle size distribution from 2 to 10 m.

Note 2. Surface analysis of electrodes by FIB-SEM
Prior FIB cross-section fabrication, sample surface was initially protected with 300 nm platinum (Pt) layer by "in situ" inducing Pt-organometallic gas precursor with electron beam (2kV @ 0.40 nA). Subsequently, Pt layer thickness was increased up to 1 μm by "in situ" inducing Pt gas precursor with Ga+ ion beam (30 kV @ 0.23 nA). Cross-sections were made using focused Ga + ions at 30 kV @ 9.30 nA with sequential reducing currents down to 0.40 nA for the case of final ion polishing step. Detailed morphological information and phase contrast images were obtained by using in-column TLD detector (SE and BSE mode) at low energy pre-monochromated electron beam (1 kV @ 50 pA, UHR, U-mode).

EDX elemental distribution analysis
The elemental composition of the pristine electrode, surface and cross-section is presented in Figure S10. The EDX mapping shows a homogenious distribution of the carbon and fluorine from the binder. The EDX of the surface has the similar chemical composition as the crosssectional EDX (Figures S10a and S10b) S26 Figure S15 Heat treatment process flow rate.